A098988 Denominators in series expansion of log(Product_{m>=1} (1+q^m)).

1, 1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 3, 13, 7, 5, 16, 17, 18, 19, 10, 21, 11, 23, 6, 25, 13, 27, 7, 29, 5, 31, 32, 11, 17, 35, 36, 37, 19, 39, 20, 41, 21, 43, 11, 15, 23, 47, 12, 49, 50, 17, 26, 53, 27, 55, 7, 57, 29, 59, 5, 61, 31, 63, 64, 65, 11, 67, 34, 23, 35, 71, 72, 73, 37, 75, 19, 77, 39, 79, 40, 81, 41, 83, 21

Offset

0,3

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Formula

Denominators of Sum_{d|n} ((-1)^(d+1))/d. - Ridouane Oudra, Apr 28 2019

Denominators of coefficients in expansion of Sum_{k>=1} (-1)^(k+1) * x^k / (k * (1 - x^k)). - Ilya Gutkovskiy, Aug 04 2023

Example

q + (1/2)*q^2 + (4/3)*q^3 + (1/4)*q^4 + (6/5)*q^5 + (2/3)*q^6 + (8/7)*q^7 + (1/8)*q^8 + (13/9)*q^9 + ...

Prog

(PARI) A098988(n) = if(0==n, 1, denominator(sumdiv(n, d, ((-1)^(d+1))/d))); \\ Antti Karttunen, May 06 2022

Crossrefs

Cf. A098987 (numerators), A353688 (n / a(n)).

Sequence in context: A053585 A305007 A353667 * A274346 A345993 A330691

Adjacent sequences: A098985 A098986 A098987 * A098989 A098990 A098991

Keyword

nonn,frac

Author

N. J. A. Sloane, Oct 24 2004

Extensions

Data section extended up to term a(84) by Antti Karttunen, May 06 2022

Status

approved